Tikhonov-Fenichel reduction for parameterized critical manifolds with applications to chemical reaction networks

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We derive a reduction formula for singularly perturbed ordinary differential equations (in the sense of Tikhonov and Fenichel) with a known parameterization of the critical manifold. No a priori assumptions concerning separation of slow and fast variables are made, or necessary. We apply the theoretical results to chemical reaction networkswith mass action kinetics admitting slow and fast reactions. For some relevant classes of such systems, there exist canonical parameterizations of the variety of stationary points; hence, the theory is applicable in a natural manner. In particular, we obtain a closed form expression for the reduced system when the fast subsystem admits complex-balanced steady states
Original languageEnglish
JournalJournal of Nonlinear Science
Issue number4
Pages (from-to)1355-1380
Number of pages26
Publication statusPublished - 2020

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